Smooth curves on a cone which pass through its vertex
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Abstract
We obtain results concerning the existence of smooth curves on the cone over a (possibly singular) plane curve. As an application, these results are used to prove the existence of certain smooth space curves which are the set-theoretic complete intersection of a cone with some other surface.
Keywords
Tangent Vector Smooth Curve Complete Intersection Tangent Line Characteristic Zero
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References
- [1]Catanese, F.: Babbage's conjecture, contact of surfaces, symmetric determinantal varieties and applications,Invent. Math. 63 (1981), 433–465MATHCrossRefMathSciNetGoogle Scholar
- [2]Cayley, A.: Considérations générales sur les courbes en espace,Comptes Rendus 54 (1862), 55–60, 396–400, 672–678Google Scholar
- [3]Gallaratti, D.: Ricerche sul contatto di superfiche algebriche lungo curve,Académie royale de Belgique, Classe des Sciences, Mémoires, Collection in-8o 32 (1960), 1–78Google Scholar
- [4]Gruson, L., R. Lazarsfeld and C. Peskine: On a theorem of Castelnuovo and the equations defining space curves,Invent. Math. 72 (1983), 491–506MATHCrossRefMathSciNetGoogle Scholar
- [5]Gruson, L. and C. Peskine: Genre des courbes de l'espace projectif, inAlgebraic Geometry: Proceedings, Tromsø Norway 1977, Lecture Notes in Mathematics,687, Springer-Verlag, (New York), 1978, pp. 31–59Google Scholar
- [6]Hartshorne, R.:Algebraic Geometry, Springer-Verlag, (New York), 1977MATHGoogle Scholar
- [7]—: Complete intersections in characteristicp>0,Amer. J. Math. 101 (1979), 380–383MATHCrossRefMathSciNetGoogle Scholar
- [8]Jaffe, D. B.:Curves on Cones, PhD Thesis, University of California at Berkeley, 1987Google Scholar
- [9]—: Space curves which are the intersection of a cone with another surface,Duke Math. J. 57 (1988), 859–876MATHCrossRefMathSciNetGoogle Scholar
- [10]—: On set theoretic complete intersections in ℙ3,Math. Ann. 285 (1989), 165–173, 175, 174, 176CrossRefMathSciNetGoogle Scholar
- [11]Jaffe, D. B.: Applications of iterated curve blowup to set theoretic complete intersections in ℙ3, submitted for publicationGoogle Scholar
- [12]Piene, R.: Cuspidal projections of space curves,Math. Ann. 256 (1981), 95–119MATHCrossRefMathSciNetGoogle Scholar
- [13]Rao, A. P.: On self-linked curves,Duke Math. J. 49 (1982), 251–273MATHCrossRefMathSciNetGoogle Scholar
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© Springer-Verlag 1991